Epidemic spreading on adaptively weighted scale-free networks

Abstract

We introduce three modified SIS models on scale-free networks that take into account variable population size, nonlinear infectivity, adaptive weights, behavior inertia and time delay, so as to better characterize the actual spread of epidemics. We develop new mathematical methods and techniques to study the dynamics of the models, including the basic reproduction number, and the global asymptotic stability of the disease-free and endemic equilibria. We show the disease-free equilibrium cannot undergo a Hopf bifurcation. We further analyze the effects of local information of diseases and various immunization schemes on epidemic dynamics. We also perform some stochastic network simulations which yield quantitative agreement with the deterministic mean-field approach.

A Literature Review of Social Network Analysis in Epidemic Prevention and Control

“…Analyzing the spread of epidemics under social networks will generally be combined with infectious disease models for analysis. For example, Zhou et al [18] and Lou and Ruggeri [19] used SI models for simulation analysis on scale-free networks; Silva et al [20], Small et al [21], and Sun et al [22] used SIS models to simulate the spread of epidemics and conduct related research and analysis; Chen et al [23], Liu and Zhang [24], Gong et al [25], Zhao et al [26], and Madar et al [27] combined dynamic SIR epidemiological models to study the spread of epidemics and the impact of immune strategies on the spread of the pathogen in multiple networks; used by Nian et al [28] and Huo et al [29], the SIRS epidemic model has been theoretically verified and computer simulated on the scale-free network to establish a more realistic model.…”

Reliability Analysis of Large-Scale Adaptive Weighted Networks

“…It was found that greater interacting strengths lead to higher epidemic thresholds, lower average disease densities of steady-state and shorter epidemic prevalent decay durations. Sun et al [32] studied the spread of epidemic diseases in adaptively weighted scale-free networks. Hu et al [33] changed the weights of links in an adaptive weighted network to balance the trade-off between the overall infection level and individual weight adaptation cost.…”

“…Despite the adaptive weighted networks have been increasingly studied in different contexts of epidemics [19,32], social network [31,33], and computer network [18], a rigorous analysis of reliability of the networks capable of rewiring is yet to be delivered in the literature. The impact of rewiring weighted links on the reliability of the networks has not been understood.…”

Markov-based solution for information diffusion on adaptive social networks

“…However, the structure of the underlying network on which information spreads always changes with time, which may influence the diffusion of information spreading significantly. To date, the adaptive behaviors, which originated in epidemic spreading [19,20] , are the most accepted assumption with which to illustrate these dynamic interactions, in which people may change their interactions in the network to protect themselves or others from being infected, with the general realization that such adaptive behaviors would suppress the diffusion process [21][22][23] . The case in information spreading would be more complicated; for example, one may sometimes contact or make mention to strangers with the purpose of spreading information or selling products on the social network, or one may also disconnect from the people who are spreading information on the network to prevent oneself from being disturbed [24,25] ; these kinds of adaptive behaviors would have an adverse impact on the spreading process.…”